Abstract
In the present thesis we study several schemes where the detection of the emitted lightfrom an atomic ensemble gives information about the state of the atoms.
A weak probe field drives the atoms such that its effect on the atomic evolution can be neglected.
The scattered light is then measured as a function of various parameters such as scattering angle frequency intensity etc.
The motivation for this route to investigate ultracold atomic gases is manifold.
Several theoretical works pointed out that the observation of
photons scattered by ultracold atoms may provide complementary
information on the quantum state of the
atoms, which could be non-destructive in some
setups.
Hence they may allow for feedback schemes,
which ultimately could lead to quantum state transfer between the light and the atoms.
Another point is that optical detection
gives in situ information about the state of the atomic ensemble.
In chapter 1 we review the basic theory for the light matter interaction
in second quantized.
The theory presented in this chapter forms the basis for our investigations of light
scattering from ensembles of ultracold atoms.
We also make some comments about the validity of the approximations and possible
ways for improvement.
In chapter 2 we show how
conservative potentials for the atoms, such as dispersive optical lattices, can be realized experimentally
due to the dispersive interaction with a far detuned laser
We then review some basic properties of the physics of a particle in
a periodic potential.
We show that the ground state and the lowest lying excitations of a
Bose-Einstein condensate in a dispersive optical lattice can be
described by the Bose-Hubbard Hamiltonian. We end the chapter by presenting some
theoretical techniques to perturbatively calculate the excitation spectrum
and the eigenstates of the Bose-Hubbard Hamiltonian,
which will be used in the following chapters.
In chapter 3 we study the photonic bandstructure of a
chain of fixed pointlike atoms
in a biperiodic configuration. We calculate the photonic spectra and the probe
transmission if the atoms are in free space and inside a standing wave optical resonator,
thereby extending the results of who considered the case of a monochromatic optical lattice.
We study how the photonic spectra are modified as a function of
the interparticle distance. By measuring the transmitted light signal we show how
one can get information about the atomic configuration.
We end the chapter with a discussion of the results obtained.
In chapter 4 we consider light scattering from ultracold atoms in an optical lattice
where we calculate the photonic scattering cross section as a function of energy and direction of emission along the Mott-insulator-superfluid phase transition.
We take into account
the finite tunneling rate for the atoms, when evaluating the scattering cross section
of the photons and the effect of photon recoil onto the atoms. The interference between the finite atomic
tunneling rate and the photon induced hopping is visible in the
heights of the Bragg peaks and we show that this effect is measurable in the superfluid phase.
We compare our analytical results using the techniques presented in Chapter 2
with numerical results where we diagonalize exactly the Bose Hubbard
Hamiltonian for a small number of atoms and wells.
We end the chapter with a discussion of our results.
In chapter 5 we consider a gas of ultracold atoms trapped at two spatially separated regions in space.
Using a two Raman lasers to couple atoms out of the systems we show that it is possible to
measure the mean value of the atomic field operator of the two systems
by measuring the scattered light intensity of one of the Raman lasers.
We compare our general theory to experimental results
and find good qualitative agreement between experimental data and our theoretical results.
We then show how this setup might be used to measure the temperature of a Bose-Einstein condensate and
to monitor the superfluid to Mott-insulator phase transition for a gas of ultracold atoms in an optical lattice.
We end the chapter with a discussion of the results obtained.
| Date of Award | 2 Feb 2011 |
|---|---|
| Original language | Spanish |
| Supervisor | Giovanna Morigi . (Director), Wolfgang Wolfgang Schleich (Director) & Gaspar Orriols Tubella (Tutor) |